Effect of intracellular diffusion on current--voltage curves in potassium channels

Abstract

We study the effect of intracellular ion diffusion on ionic currents permeating through the cell membrane. Ion flux across the cell membrane is mediated by special proteins forming specific channels. The structure of potassium channels have been widely studied in recent years with remarkable results: very precise measurements of the true current across a single channel are now available. Nevertheless, a complete understanding of the behavior of the channel is still lacking, though molecular dynamics and kinetic models have provided partial insights. In this paper we demonstrate, by analyzing the KcsA current-voltage currents via a suitable lattice model, that intracellular diffusion plays a crucial role in the permeation phenomenon. The interplay between the selectivity filter behavior and the ion diffusion in the intracellular side allows a full explanation of the current-voltage curves.

Residence time estimates for asymmetric simple exclusion dynamics on strips

“…The efficiency of transport of active matter in microscopic systems is an issue of paramount importance in a number of fields of science including biology, chemistry, and logistics. Looking particularly at drug-delivery design scenarios [22], ion moving in molecular cytosol [2][3][4], percolation of aggressive acids through reactive porous media [17], the traffic of pedestrians in regions with drastically reduced visibility (e.g., in the dark or in the smoke) [10,11,24] (see also the problem of traffic of cars on single-lane highways [27]), we see that the efficiency of a medical treatment, the properties of ionic currents thorough cellular membranes, the durability of a highly permeable material, or the success of the evacuation of a crowd of humans, strongly depends on the time spent by the individual particle (colloid, ion, acid molecule, or human being) in the constraining geometry (body, molecule, fabric, or corridor).…”

Singular kernel problems in materials with memory

“…h Proof of Theorem 2 (uniqueness of the solution admitted by (25) and by (35)) The thesis is proved by contradiction; thus, assume v andṽ; v 6 ¼ṽ; both satisfy the linear equation (25). Then, also w :¼ v Àṽ; as any linear combination of v andṽ; is a solution of the same equation.…”

“…Note that the proof is unified since, on use of linearity, given two different solutions v andṽ; of any of the two Eqs. (25) or (35), then their difference is again a solution. In addition, let w :¼ v Àṽ; it follows to satisfy…”

“…This is the case studied, again in 2014, by Deseri et al [9], who show how a fractional derivative model can be adapted to describe bio-materials. Indeed, the Special Issue of Discrete and Continuous Dynamical Systems-Series B dedicated to Mauro Fabrizio [10], comprises articles dedicated to materials with memory or which may be termed new, such as [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and mathematical models to describe the behaviour of problems which arise in biological contexts [25][26][27][28]. These results motivate us to adopt, in this present article, less restrictive functional requirements on the kernel.…”

Simple diffusion hopping model with convection

“…An extensively used algorithm for these studies is the particle hopping model where particles can hop between discrete cells on a lattice subject to specific movement rules or by diffusing to adjacent unoccupied cells [1]. Particle hopping models have been applied to study a variety of systems such as particle transport in disordered media [2,3], diffusion at material interfaces [4,5], the diffusion of large particles in unentangled polymer solids [6], water diffusion in cell suspension systems [7], traffic flows [8][9][10], ion transport through biological membranes [11,12], biological systems involving the movement of animals, micro-organisms or cells [13], and particle residency times in two-dimensional vertical strips [14].…”